Yes, I can see that the QF site is not looking good for those dates. 31st has much better options, while 28th is very limited.
No harm phoning the Call Centre to enquire. Not much to lose other than massive time-wasting and potentially wrong information being provided. At some point you will be phoning them anyway. If you are lucky, Oz or NZ may answer (this sometimes works at around 6.30am or earlier, but no guarantees), but SA and Manila never sleep.
The trouble is that the CSO will only work from what they can see as being available. Can be frustrating. Never any point getting into an argument though.
Personally, when I see something that will work, even if not perfect, I book it. I can always change later if I become aware of something better, at 5,000 points cost per person, per phone call of course. Hesitation can lose the seats, and then what? Only you can decide when to book of course.
Edit: As for connection times, I am happy with 90 minutes to (ideally) two hours). But all that goes out the window when the unforeseen cancellations/late arrivals come along. Some prefer very short connections (easier with HLO), but we are all different.